Find all possible equations of the parabolas described

Dad

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Nov 27, 2006
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:?: Please help.
I cannot even get started on these...
Instructions - Find all possible equations of the parabolas described.

1. The parabola is tangent to the x-axis, has y-intercept 18, and passes through
the point (2,8) (2 possibilities)

2. The vertex of the parabola is on the line y=20, the y-intercept is 15, and 3
is a zero of the equation of the parabola. (2 possibilities)

Dad
 
1) The "tangent" part tells you that the vertex must lie on the x-axis (so k = 0), and the y-intercept gives you the constant term (so c = 18). You might want to draw a graph, to get started. See if you can figure out, roughly, where the parabolas must be.

Plug the known value (c = 18) and the known point ((x, y) = (2, 8)) into the general quadratic equation, y = ax<sup>2</sup> + bx + c. You should end up with a quadratic in "x", which you can solve for the x-values of the two possible vertices.

2) The vertex is of the form (x, y) = (x, 20), but you don't have the "x" yet. The y-intercept gives you the point (0, 15), so you have the constant term. And you know that (3, 0) is a point on the parabola. With this information, solve for the two x-values, just as in (1).

If you get stuck, please reply showing what you have tried. Thank you.

Eliz.
 
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